Mathematical modeling and control of pH processes are quite challenging since the processes are highly nonlinear, due to the logarithmic relationship between the concentration of hydrogen ions [H+] and pH level. The transfer function from input pH to output pH is
where we assume a delay of 3.3 seconds. Ga(s) is a model for the anaerobic process in a wastewater treatment system in which methane bacteria need the pH to be maintained in its optimal range from 6.8 to 7.2 (Jiayu, 2009). Similarly, (Elarafi, 2008) used empirical techniques to model a pH neutralization plant as a second-order systemwith a pure delay, yielding the following transfer function relating output pH to
input pH:
where we assume a delay of 25 seconds.
a. Find analytical expressions for the unit-step responses ya(t) and yp(t) for the two processes, Ga(s) and Gp(s).
b. Use Simulink to plot ya(t) and yp(t) on a single graph.
